I remember when I played this room - it took me hours to figure it out.
Hint:
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× It is possible to enter and exit force arrows in five of the eight directions
Spoiler:
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× You travel sideways along the rows of force arrows and end up at the bottom
I don't think this room is mentioned on the Hints page on the website, and I really think it should.
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Slashing, whirling, diving, twirling,
Snapping, turning, rising, swirling,
Screeching, flipping, gliding, sliding,
The red hawk's dance of death.
.....the king of the skies.....